Final answer:
To find the area of the quadrilateral, we divide it into two triangles and use the formula for the area of a triangle. By calculating the areas of the two triangles and summing them up, we find that the area of the quadrilateral is 100 square units.
Step-by-step explanation:
To calculate the area of a quadrilateral, we can divide it into two triangles and find the area of each triangle using the formula for the area of a triangle: A = (1/2) * base * height.
First, let's find the area of the triangle formed by the vertices (6,3), (-6,5), and (-2,-5). The base of this triangle is the distance between (-6,5) and (-2,-5), which is 10 units. The height can be found by drawing a perpendicular line from (-2,-5) to the line connecting (-6,5) and (-2,-5), which is also 10 units.
Using the formula for the area of a triangle, we can calculate the area of this triangle as: A = (1/2) * 10 * 10 = 50 square units.
Next, let's find the area of the triangle formed by the vertices (-2,-5), (5,-3), and (6,3). Using the same method as before, we can find the base as the distance between (-2,-5) and (6,3), which is 10 units. The height can be found by drawing a perpendicular line from (-2,-5) to the line connecting (5,-3) and (6,3), which is also 10 units.
Using the formula for the area of a triangle, we can calculate the area of this triangle as: A = (1/2) * 10 * 10 = 50 square units.
The total area of the quadrilateral is the sum of the areas of the two triangles: 50 + 50 = 100 square units.
Therefore, the correct answer is D. 100 square units.